A latent, quasi-independent truncation time is assumed to be linked with the observed dependent truncation time, the event time, and an unknown transformation parameter via a structural transformation model. The transformation parameter is chosen to minimize the conditional Kendall's tau (Martin and Betensky, 2005) <doi:10.1198/016214504000001538> or the regression coefficient estimates (Jones and Crowley, 1992) <doi:10.2307/2336782>. The marginal distribution for the truncation time and the event time are completely left unspecified. The methodology is applied to survival curve estimation and regression analysis.
